A sum of money was distributed equally in a class of boys. Had there been 10 boys more, each would have received a rupee less. If there had been 15 boys less, each would have received 3 rupees more. Find the sum of money and the number of boys. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Let the number of boys be

and the total sum of money be

rupees.
Sum of money received by each boy

Here, the number of boys becomes

.
Sum of money received by each boy

The sum of money received by each boy (where the number of boys is

) is Re. 1 less than the sum of money received by each boy (where the number of boys is

).
Therefore, we get the equation

Simplifying by cross multiplication, we get

Multiplying

using the distributive law of multiplication, we get

Subtracting

from both sides, we get

Rewriting the equation, we get

Sum of money received by each boy

The sum of money received by each boy (where the number of boys is

) is Re. 1 less than the sum of money received by each boy (where the number of boys is

).
Therefore, we get the equation

Simplifying by cross multiplication, we get

Multiplying

using the distributive law of multiplication, we get

Subtracting

from both sides, we get

Dividing both sides by 3 and rewriting the equation, we get

Subtracting equation

from equation

, we get

Adding and subtracting the like terms, we get

Dividing both sides by 5, we get

Substituting

in the equation

,we get

Subtracting

from both sides, we get

Thus, the number of boys is 40.
Substituting

in the equation

, we get

The total sum of money is Rs. 200.
So, option 2 is correct.

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